Quasi-two-body $B_{(s)}\to V \pi\pi$ Decays with Resonance $f_0(980)$ in PQCD Approach

TL;DR

This paper investigates quasi-two-body B meson decays involving the resonance $f_0(980)$ using perturbative QCD, calculating branching fractions and CP asymmetries, and comparing results with experimental data.

Contribution

It introduces a new wave function for the $s$-wave $\pi^+\pi^-$ pair and analyzes the impact of the $f_0(980)$ mixing angle on decay predictions.

Findings

Calculated branching fractions agree with experimental data for certain mixing angles.

Predicted branching fractions for other decay modes are accessible to current experiments.

Estimated isospin-related decay branching fractions are approximately half of the charged-pion modes.

Abstract

Motivated by the measurements of branching fractions of the quasi-two-body decays $B^0\to K^{*0}(f_0(980)\to )\pi^+\pi^-$ and $B^0\to \rho^0(f_0(980)\to )\pi^+\pi^-$, we study the charmless $B\to V (f_0(980)\to ) \pi^+\pi^-$ decays in the perturbative QCD approach. Supposing that $f_0(980)$ is a two-quark state and mixture of $n\bar n=(u\bar u+d\bar d)/\sqrt 2$ and $s\bar s$ with the mixing angle $\theta$, we calculate the branching fractions of these decays with the new introduced $s$-wave $\pi^+\pi^-$-pair wave function. When the mixing angle $\theta$ lies in the range $[135^{\circ}, 155^{\circ}]$, the calculated branching fractions of the $B^0\to K^{*0}f_0(980)\to K^{*0}\pi^+\pi^-$ and $B^0\to \rho^0f_0(980)\to \rho^0\pi^+\pi^-$ decays are in agreement with the experimental data. The branching fractions of other decays could be measured in the current LHCb and Belle II experiments. Considering the isospin symmetry, we also estimate the branching fractions of the quasi-two-body decays $B\to Vf_0(980)\to V\pi^0\pi^0$, which are half of those the corresponding decays $B\to Vf_0(980)\to V\pi^+\pi^-$. Moreover, the direct $CP$ asymmetries of these decays are also calculated, and some of them can be tested in the current experiments.